1. Field of the Invention
The present invention relates to a strain wave gearing, and more particularly to an improvement in tooth profile of a circular spline used in the strain wave gearing which comprises a first rigid circular spline, a second rigid circular spline juxtaposed with the first spline along the axis of the first spline and having a different number of teeth from that of the first spline, a flexspline coaxially disposed inside the two circular splines in engagement with the circular splines and having the same number of teeth as the first circular spline, and a wave generator for bending and deforming the flexspline to bring it into partial engagement with the respective teeth of both circular splines and for rotating the deformed configuration of the flexspline whereby the wave generator is rotated to produce a relative rotation between the first and second circular splines.
2. Description of Prior Art
The strain wave gearing is well known, as seen from U.S. Pat. No. 2,906,143 granted to Musser. A typical strain wave gearing comprises a rigid circular spline, a flexspline disposed inside the circular spline, the flexspline being deformable into, for example, an elliptic configuration to bring the flexspline into an engagement with the circular spline at two points and further having a number of teeth which is larger or smaller than that of the circular spline by 2 n ("n" being a positive integer), and a wave generator disposed in the flexspline to deform the flexspline to, for example, an elliptic configuration so as to bring the flexspline into engagement with the circular spline at the two points on the major axis of the ellipsoid. The wave generator includes an elliptic cam plate and a ball bearing fittingly mounted on the outer periphery of the cam plate. The outer race of the bearing is inserted into the flexspline to deform the flexspline to the elliptic shape. In the strain wave gearing as mentioned above, the input shaft fixed to the cam plate of the wave generator is rotated while the ellipsoid of the flexspline is rotated. Upon rotating the ellipsoid, one of the flexspline and the circular spline is rotated relative to the other by an amount that is in proportion to the difference in the number of teeth between the two splines. Where an output shaft is mounted on either the flexspline or the circular spline, the output shaft is rotated very slowly in comparison with the input shaft. Thus, the strain wave gearing has frequently been applied to precision machinery because in the gearing, a high reduction ratio is obtained in spite of a small number of elements used therefor.
Recent modifications have been made with respect to the teeth used in a strain wave gearing so as to improve the engagement characteristics of the teeth to obtain good performance and increase the load capacity. The basic gear tooth is disclosed in detail in U.S. Pat. No. 3,415,143 granted to Ishikawa. The Ishikawa patent teaches that an involute tooth shape is applied to the gearing. Thus, the elliptic flexspline is engaged with the circular spline only at the two points out of the major axis of the ellipsoid, resulting in lowering the allowable transfer torque.
If the tooth of the Ishikawa patent is applied to the strain wave gearing, however, it is difficult to bring the flexspline into a continuous engagement with the circular spline until the tooth of one of the splines is completely separated from that of the other. More specifically, in the case of a zero or negative deviation as shown in the curves a and c of FIG. 4 of the Ishikawa patent, the flexspline engaging with the rigid circular spline has a movement locus of the typical point of the tooth thereof (except for a small portion of the top of the curve c), the locus being concave with respect to the circular spline. In order to obtain continuous contact between both splines, it is necessary that the profile of the tooth of the circular spline must be formed convex in shape, unlike the linear tooth and the involute tooth. Where the movement locus of the typical point of the flexspline is convex (positive deviation) as shown in the curve b of FIG. 4 of the Ishikawa patent, deflection of the flexspline increases and then the bending stress increases. Thus, it is disadvantageous in that the available range of the locus is small and that there are few teeth which are in mesh with each other. There is room for improving the strain wave gearings of the Ishikawa patent with regard to allowable transfer torque.
To this end, one of the inventors, Ishikawa, has made an improvement of the strain wave gearing, as shown in the above-mentioned U.S. Pat. No. 4,823,638. In the improved strain wave gearing, the tooth faces of both the circular spline and the flexspline are formed with a convex profile while the tooth flanks thereof are formed with a concave profile, so that the continuous engagement or contact is effected by meshing the convex-shaped tooth face of one of the splines with the convex-shaped tooth face of the other spline. The strain wave gearing as mentioned above has successfully operated for a so-called cup-shaped strain wave gearing including a single rigid circular spline and a cup-shaped flexspline having the different number of teeth from the circular spline.
Meanwhile, separately from the cup-shaped gearing mentioned above, there is a type of strain wave gearing called flat-shaped strain wave gearing. The flat-shaped gearing is composed of a first rigid circular spline, a second rigid circular spline juxtaposed with the first spline along the axis of the first spline and having a different number of teeth from the first spline, a flexspline coaxially disposed inside the two circular splines in engagement with both circular splines and having the same number of teeth as the first circular spline, and a wave generator for bending and deforming the flexspline to bring the flexspline into partial engagement with the respective teeth of both circular splines and for rotating the deformed configuration of the flexspline whereby the wave generator is rotated to produce a relative rotation between the first and second splines. The reason why this strain wave gearing is called flat shaped strain wave gearing is that two circular splines are juxtaposed with each other and a flexspline formed with an annular configuration whereby the whole of the gearing is made in a thin, flat configuration.
In the flat shaped strain wave gearing, the tooth profile of the above-mentioned U.S. Pat. No. 4,823,638 can be applied to the engagement portion between the second circular spline and the flexspline having the different number of teeth to obtain the continuous engagement of the teeth therebetween. On the other hand, the same tooth profile as disclosed in the above-mentioned U.S. Pat. No. 4,823,638 cannot be applied to the engagement between the first circular spline and the flexspline having the same number of teeth because there is no relative rotation between the splines whereby a tooth of the flexspline is moved only within a space of the first circular spline.
Study has already been made on the engagement between the first circular spline and the flexspline as shown, for example, in U.S. Pat. No. 2,959,065 granted to Musser. The strain wave gearing of the Musser patent is so constructed that the first circular spline is meshed with the flexspline at specific points apart from the major axis of an elliptic wave generator. In other words, only the limited teeth are effectively engaged with each other in the whole of the gearing. Thus, it is disadvantageous in that the torque transfer amount is limited and the capacity of the torque transfer decreases.